On some sums at the $a$-points of the $k$-th derivatives of the Dirichlet $L$-functions

Authors

MOHAMMED MEKKAOUI
ABDALLAH DERBAL
KAMEL MAZHOUDA

Abstract

Let $L^{(k)}(s,\chi)$ be the $k$-th derivative of the Dirichlet L-function associated with a primitive character $\chi$ mod $q$ and $a$ be a complex number. The solutions of $L^{(k)}(s,\chi)=a$ are called $a$-points. In this paper, we give an asymptotic formula for the sums

DOI

10.3906/mat-2002-98

Keywords

Dirichlet $L$-function, $a$-points, value-distribution

First Page

1544

Last Page

1560

Recommended Citation

MEKKAOUI, M, DERBAL, A, & MAZHOUDA, K (2020). On some sums at the $a$-points of the $k$-th derivatives of the Dirichlet $L$-functions. Turkish Journal of Mathematics 44 (5): 1544-1560. https://doi.org/10.3906/mat-2002-98